November 28, 2020

The first space launch occurred October 4, 1957.

What was its name and who launched it?

  • Sputnik I, launched by the Soviet Union

One month later, on November 3, 1957, the first living being was launched into space.

  • Laika the cosmo-dog

It took four more years until the first human was launched into space on April 12, 1961.

  • Yuri Gagarin

And then another eight years for humans to set foot on our Moon on July 20, 1969.

Can you name them?

  • NASA’s Apollo 11 crew: Neil Armstrong, Michael Collins, and Buzz Aldrin

Project Goal

  • Determine the relationship between space mission success and other variables.

Space Shuttle Challenger exploded moments after launching on January 28, 1986. Source: CNN news

Data


Source: https://www.kaggle.com/agirlcoding/all-space-missions-from-1957

Exploratory Data Analysis

Launches Over Time

Exploratory Data Analysis

Launch Organizations

Exploratory Data Analysis

Launch Organizations

Exploratory Data Analysis

Launch Countries

Exploratory Data Analysis

Outcome Variable: Launch Success (92%)

Exploratory Data Analysis

Outcome Variable: Launch Success Over Time

Exploratory Data Analysis

Outcome Variable: Launch Success by Country

Exploratory Data Analysis

Outcome Variable: Launch Success by Organization

Method

  • Categorical Data Analysis with Logistic Regression \[\displaystyle logit(\pi) = log \left( \frac{\pi}{1- \pi} \right) = \beta_0 + \beta_1 X_{1} + \beta_2 X_{2} + \ldots + \beta_k X_{k}\]

  • Single Logistic Regression models \[\displaystyle logit(\pi) = log \left( \frac{\pi}{1- \pi} \right) = \beta_0 + \beta_1 X_{1}\]

    • Response variable: Mission Outcome (Success: Yes/No)

    • Predictors: Rocket Status (Active/Retired), Country (USA/Russia), Space Race Decade (1960s/1970s)

Inferences

  • Hypothesis test for the slope
    • Test whether the groups/levels in the explanatory variable differ in chance (odds) of success

\(H_o:\) \(\beta_1 = 0\)

\(H_a:\) \(\beta_1 \ne 0\)

Test statistic: \(\displaystyle z = \frac{\hat{\beta_1}}{s(\hat{\beta_1})}\)

p-value = 2*pnorm(z, lower.tail = FALSE)

  • Confidence interval

\[\hat{\beta_1} \pm z_{({1 - \alpha/2})} s(\hat{\beta_1})\]

Mission Status vs Rocket Status

  • Is there a difference in the chance of success between active and retired rockets?

Mission Status vs Rocket Status

  • Model \[logit(Pr(Success)) = 2.084 + 0.528 \cdot Active\]
             Estimate Std. Error   z value    Pr(>|z|)
(Intercept) 2.0842255 0.05362567 38.866192 0.000000000
ActiveYes   0.5280206 0.15084041  3.500525 0.000464343
  • Untransform (exponentitate) slope to get odds ratio
ActiveYes     2.5 %    97.5 % 
 1.695573  1.272852  2.301764

USA vs Russia

  • Do the two countries have the same chance of space mission success?

USA vs Russia

  • Model \[logit(Pr(Success)) = 2.016 + 0.319 \cdot Russia\]
              Estimate Std. Error  z value Pr(>|z|)
(Intercept)    2.01575    0.08469 23.80166  0.00000
CountryRussia  0.31928    0.11446  2.78945  0.00528
  • Inferences
CountryRussia                       2.5 %        97.5 % 
    1.3761360     0.5791487     1.0988476     1.7216396

Space Race Decades: 1960s and 1970s

Apollo 11

Space Race Decades: 1960s and 1970s

  • Do the two decades differ in terms of successful rate of space mission?

Space Race Decades: 1960s and 1970s

  • Model \[logit(Pr(Success)) = 1.329 + 1.211 \cdot Decade1970s\]

  • Inferences

Decade1970s       2.5 %      97.5 % 
   3.355326    2.512054    4.519424

Which model gives us best prediction?

  • AIC (Akaike’s Information Criterion)

  • The smaller the AIC, the better the model

Summary

  • Active rockets have greater chance of success than retired rockets

(OR = 1.696, 95% CI (1.273, 2.302))

  • Russia is more likely to have successful space missions than USA

(OR = 1.376, 95% CI (1.099, 1.722))

  • There’s an increase in success rate from 1960s to 1970s

(OR = 3.355, 95% CI (2.512, 4.519))

Future Work

  • Time Series Analysis
  • Mixed Models
  • Spatial Visualization

Thanks!